Method and device for providing timing information in a wireless communication system

ABSTRACT

A method and a device of providing timing information within a wireless communication system is described. The timing information is extracted from a received transmit signal. The inventive method comprises the steps of providing a training signal on the receiver side relating to a known signal portion of the transmit signal, scaling the training signal, quantizing the scaled training signal, correlating one or more parts of the received transmit signal with the scaled training signal to obtain one or more correlation results, and determining the timing information on the basis of the correlation results.

This application is a continuation of PCT International Application No.PCT/EP02/05614, filed in English on 22 May 2002, which designated theU.S. PCT/EP02/05614 claims priority to EP Application No. 0115679.1filed 04 Jul. 2001. The entire contents of these applications areincorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Technical Field

The invention relates to a method and a device of providing timinginformation in a wireless communication system and more particularly toefficient timing synchronization on the basis of a transmit signalhaving a signal portion known on the receiving side.

2. Description of the Prior Art

The provision of timing information is an essential feature of wirelesscommunication systems which allows to ensure synchronicity among thedistributed system components. In almost every wireless communicationsystem the timing information is obtained from a transmit signalanalyzed on a receiving side.

In the following, an approach for extracting timing information from aninput signal is exemplarily described for wireless communication systemsoperating in accordance with Orthogonal Frequency Division Multiplexing(OFDM).

OFDM is a multicarrier modulation scheme which is especially suited forhighly frequency-selective transmission channels such as typicalchannels for mobile communication systems or for high-rate wiredtransmission via copper lines. Highly frequency-selective channels arecharacterized by impulse responses which are substantially longer thanone sample interval. Therefore, each received sample in a digital baseband domain is a superposition of several transmit samples weighted bythe respective channel coefficients. This means that highlyfrequency-selective channels are subject to intersample interference.

The principle of OFDM to combat intersymbol interference is to dividethe total channel bandwidth into substantially smaller portions, i.e.subchannels. A sequence of samples to be transmitted is combined to asingle OFDM symbol and transmitted in parallel on these subchannels. Asingle OFDM symbol thus uses all of the subchannels in parallel. Inaccordance with OFDM, transmitted subchannel signals are orthogonal toeach other.

Since the duration of one OFDM symbol is much longer than the sampleinterval, intersymbol interference is strongly reduced.

To further reduce intersymbol interference, usually a guard interval isintroduced between two OFDM symbols which are to be consecutivelytransmitted. If the length of the guard interval exceeds the length ofthe channel impulse response, there is no residual intersymbolinterference. Furthermore, if the guard interval is constituted by arepeated signal portion, e.g. a cyclic prefix, a very simpleequalization of the frequency-selective channels in the frequency domainis possible.

However, since the use of a guard interval leads to additionaltransmission overhead, the length of the guard interval is usuallychosen such that the intersymbol interference is not totally cancelled.Rather, only the main contributions of typical channels are accommodatedin the guard interval and residual intersymbol interference istolerated.

An OFDM receiver has to perform synchronization prior to demodulation ofthe subcarriers. The task during synchronization is to find an optimaltiming for minimizing the effects of intersymbol interference.Therefore, timing information allowing to find out the optimal timinginstant for synchronization purposes has to be provided.

Several synchronization approaches are known in the art. Most of theseapproaches are based on the exploitation of repeated signal portionswithin a transmit signal. Usually, the repeated signal portions arelocated at predefined locations of a so-called repetition preamble. Anexample for synchronization of OFDM systems based on a repetitionpreamble is described in M. Speth, F. Classen and H. Meyr, FrameSynchronization of OFDM Systems in Frequency Selective Fading Channels,VTC '97, Phoenix.

In an OFDM receiver the received sample stream is processed in order torecognize the repeated signal portion. Several metrics to detectrepetition preambles for synchronization purposes are exemplarilydescribed in S. Müller-Weinfurtner, On the Optimality of Metrics forCoarse Frame Synchronization in OFDM: A Comparison, PIMRC '98, Boston.These metrics make use only of the cyclic nature of the repeated signalportion but not of the actual content thereof.

A synchronization method which actually exploits the content of arepeated signal structure is known from R. van Nee, R. Prasad, OFDM forwireless multimedia communications, Artech House, 2000. According tothis synchronization method, a matched-filter approach is pursued toachieve optimal timing synchronization for OFDM in a multipathenvironment. During matched filtering a special OFDM training signalderived from a transmit signal portion is used for which the datacontent is known to the receiver. In the matched filter, a receivedtransmit signal is correlated with the known OFDM training signal. Theresulting matched filter output signal comprises correlation peaks fromwhich both timing information and frequency offset information can bederived.

The filter tap values used during matched filtering are obtained fromtraining values comprised within the known OFDM training signal.According to a first approach, the filter tap values equal thetransmitted training values. According to a second approach, the filtertap values are derived from the training values by means ofquantization. Quantization reduces the overall complexity of the matchedfilter since the multiplications necessary during the correlationoperations can thus be reduced to additions.

By means of quantization, each of the real part and the imaginary partof the training values is mapped separately on the nearest integer fromthe set of {−1, 0, 1}. The quantization is thus performed individuallyfor the real and imaginary parts. This means that after quantization thefilter tap values will usually also comprise a real and an imaginarypart each. This leads to four additions per correlation operation. Thenumber of zeros in the resulting set of quantized values is fixeddepending on the individual training values comprised within thetraining signal.

There is a need for a method and a device for providing timinginformation for a received transmit signal which allow derivation of thetiming information in an efficient and flexible manner.

SUMMARY

The need is met using a method of providing time information for areceived transmit signal; the method comprises: providing on a receivingside a training signal relating to a known signal portion of thetransmit signal, scaling the training signal, quantizing the scaledtraining signal, correlating one or more parts of the received transmitsignal with the scaled training signal to obtain one or more correlationresults, and determining the timing information on the basis of thecorrelation results. Preferably, the provided timing information is anoptimum timing instant for synchronization purposes. The timing instantcan be optimum e.g. with respect to minimizing the interference power.

The signal portion of the transmit signal based on which the trainingsignal is derived can be repeated in the transmit signal, i.e. thetransmit signal may comprise a cyclic structure. Such a repeated signalportion in the transmit signal will increase the performance of thecorrelation. Preferably, the training signal is deduced from arepetition preamble of the transmit signal.

The scaling of the training signal has the advantage that it allows tocontrol the outcome of the quantization and to influence the complexityof the subsequent correlation. Since the correlation capacity which isneeded to be implemented depends on the number of quantized trainingvalues the real and imaginary parts of which are mapped on specificvalues like zero, the complexity of the correlation becomes adjustable.For example, a high number of zeros implies a low correlationcomplexity. Thus, scaling enables a flexible trade-off between highperformance correlation (few zeros) and low complexity correlation (manyzeros).

The scaling factor can be either fixed or variable. The smaller thescaling factor, the more zeros will be contained within the quantizedtraining signal and vice versa.

According to a preferred embodiment, which can be implementedadditionally to or independently from the scaling operation, the realpart and the imaginary part of each training value comprised within thetraining signal are not quantized individually, but jointly. Forexample, each training value may be mapped during quantization on apredefined set of pure real and pure imaginary values. This allows toreduce the correlation operations to only two real additions permultiplication.

Preferably, the set of {0, ±1, ±j} is used for the quantization. Asmentioned previously, such a predefined set of pure real and pureimaginary values comprising the value zero is advantageous whencorrelation complexity is to be adjusted by appropriately selecting thescaling factor.

The individual correlation operations can be convolutions performed bymeans of a matched filter. The filter complexity corresponds to thepreviously discussed correlation complexity and the filter tap valuesequal the quantized training values. Of course, other correlationtechniques apart from matched filtering can be applied as well.

The correlation results obtained by means of the correlation operationshave preferably the form of estimated channel impulse responses. Due tothe quantization step, the channel impulse responses obtained bycorrelation can be regarded as approximated channel impulse responses.

Based on the estimated channel impulse responses the optimal timinginstant for synchronization purposes can be estimated. Preferably, theestimation of the optimal timing instant comprises determining a signalpower of the channel impulse response for each possible timing instant.As an example, the signal power contained in individual time windowsmoving within the receive signal can be analyzed to determine the timewindow containing the maximum signal power.

According to a further non-limiting example embodiment, which isindependent from the scaling approach outlined above, a false alarmdetection is implemented. The false alarm detection can be configured tobe a by-product of the determination of the timing information.Preferably, the false alarm detection is performed based on the maximumsignal power which is an intermediate result obtained during timingsynchronization.

By means of false alarm detection it can be checked whether the timinginformation already determined or the timing information still to bedetermined is or will be wrong. Performing false alarm detection basedon an intermediate result allows to implement a false alarm detectionscheme at almost zero additional computational or hardware complexity.Moreover, exploiting an intermediate result is advantageous from a powerconsumption point of view because it allows an early detection of afalse alarm.

The false alarm detection scheme may comprise comparing the maximumsignal power with a signal power threshold. The threshold may bedetermined based on the power of the training signal and is preferablyselected such that the rate of discarding correct timing information isdriven towards zero while having a sufficiently high detectionprobability for false alarms. The technology may be implemented as acomputer program product with program code portions for performing themethod or as a hardware solution. In the case of a computer programproduct implementation the computer program product is preferably storedon a computer-readable recording medium.

A hardware solution may be realized in the form of a receiver havingdedicated units, each unit performing one or more of the individualsteps of the inventive method.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a portion of a repetition preamble;

FIG. 2 is a schematic diagram of a transmitted repetition preamble;

FIG. 3 is a schematic diagram of a received repetition preamble having asignal portion to be correlated with a training signal; and

FIG. 4 is a schematic diagram of a receiver according to the invention.

DETAILED DESCRIPTION

The following description is exemplarily described with reference to awireless communication system in the form of a HIgh PErformance RadioLocal Area Network type 2 (Hiperlan/2). The physical layer of Hiperlan/2is based on OFDM with a guard interval in the form a cyclic prefix. Itmay be well understood, however, that the technology described alsoapplies to other OFDM transmission systems with dedicated signalportions exploitable for timing purposes as well as to non-OFDMtransmission systems having equivalent features. Above all, thetechnology described is applicable to other Wireless Local Area Network(WLAN) systems such as standardized by IEEE (U.S.A.) or MMAC (Japan).

Hiperlan/2 is a short-range high-rate data communication system whichmay be used as a WLAN system, e.g. to transport internet protocol (IP)packets. However, Hiperlan/2 is also capable to act as wirelessAsynchronous Transfer Mode (ATM) system as well as a public accesssystem, e.g. with an interface to the Universal Mobile TelecommunicationSystem (UMTS).

Hiperlan/2 is a packet-switched cellular system. In Hiperlan/2 fivedifferent kind of physical bursts (transport channels) are defined andeach physical burst is preceded by a preamble portion containing OFDMtraining information for the purposes of acquisition, synchronization,channel estimation, etc.

In Hiperlan/2 preamble portions for different physical bursts aredifferent. However, within each preamble portion there is a dedicatedpreamble part, constituted by the three OFDM symbols C32, C64 and againC64, appearing in each preamble type. This dedicated preamble part isdepicted in FIG. 1. The long symbols C64 each comprise 64 samples(N_(C64) =64) and are identical. The short symbol C32 is a copy of the32 last samples (N_(C32)=32) of the C64 symbols and can thus be viewedas a cycled prefix. Each physical burst comprises a payload portion inaddition to the preamble portion and each data-carrying OFDM symbolwithin the payload portion comprises a separate cyclic prefix CP with 16samples (N_(CP)=16). Therefore, the symbol C32 comprised within thepreamble portion can be viewed as an extended cyclic prefix with respectto the CP symbol.

In the following, an example embodiment providing timing information fora received transmit signal will be discussed in more detail for theHiperlan/2 system outlined above.

The location of the preamble samples which are involved in fine timingsynchronization are exemplarily depicted in FIGS. 2 and 3. FIG. 2 showsa part of a preamble of a transmit signal. As already described withreference to FIG. 1, the preamble comprises one C32 symbol followed bytwo C64 symbol. The preamble part depicted in FIG. 2 comprises arepeated signal portion <c> which corresponds to the first C64 symbol.Based on the standardized content of the repeated signal portion <c>,i.e. the C64 symbol, the training signal is derived by using thecomplex-value samples c[.] comprised within <c> as training samples.

FIG. 3 shows the preamble part of a receive signal which corresponds tothe preamble part of the transmit signal depicted in FIG. 2. The hatchedportion of the received preamble indicates the location of the one ormore parts of the receive signal to be correlated with the trainingsignal. The values k_(S) (which has a negative value) and k_(E) describethe location of a search window. This location depends on the initialtiming accuracy as well as on the various possible shapes of differentchannel impulse responses. Portions of the received preamble differentfrom the hatched portions may of course also be taken for correlationpurposes.

Now, an example embodiment of a receiver is described with reference toFIG. 4.

The receiver 10 of FIG. 4 comprises a unit 12 for providing a trainingsignal relating to a known content of the repeated signal portion <c> ofthe transmit signal, a unit 14 for scaling the training signal, a unit16 for quantizing the scaled training signal, and a database in the formof a Read Only Memory (ROM) 18 for storing the quantized trainingsignal. The receiver 10 further comprises a unit 20 for correlating oneor more parts of the received signal with the scaled training signal toobtain one or more correlation results, a unit 22 for determining timinginformation on the basis of the correlation results and a unit 24 fordetecting a false alarm.

The receiver 10 operates as follows. Firstly, the repeated signalportion <c> corresponding to the training signal is preprocessed toenable an efficient matched filtering and the preprocessed data isstored in the ROM 18. Secondly, a matched filtering is performed in thecorrelation unit 20 using the preprocessed data and an optimal timinginstant k_(C64) is determined in the determination unit 22.Simultaneously, false alarm detection is performed in the detection unit24.

The repeated signal portion <c>, i.e. the training signal, comprises asequence of complex-valued samples c[.] constituting training values.Since the correlation unit 20 is essentially a matched filter, thetraining values can also be referred to as (unprocessed) matched filtertap values.

Initially, the matched filter tap values c[.] are provided by the unit12 which can be a memory or some kind of interface. The matched filtertap values c[.] are first subjected to scaling within the scaling unit14. During scaling, the matched filter tap values c[.] are takenindividually and scaled by a predefined or dynamically selected scalingfactor.

The scaling factor is chosen to control the number of zero elementsproduced in the subsequent quantization operations which take placewithin the quantization unit 16. For example, a low scaling factor leadsto a high number of zeros. Thus, the correlation or filter complexitycan be adjusted.

After scaling, the scaled matched filter tap values c[.] areindividually subjected to quantization within the quantization unit 16.The quantization unit takes each scaled complex tap value c[.] and mapsit on a quantization value chosen from the predefined set of {0, ±1,±j}. This set comprises only pure real and pure imaginary values. Bymapping each scaled tap value c[.] on the set of {0, ±1, ±j}, thesequence <c> of scaled tap values c[.] is transformed into the pentenarysequence <c₅> of quantized tap values c₅[.]. By this, the complexmultiplications usually needed during matched filtering in thecorrelation unit 20 are either replaced by simple sign operations or byexchanges of real and imaginary parts or they are completely discardedin the case of scaled tap values c[.] mapped on the value c₅[K]=0.

The quantization can be performed by means of mapping a scaled tap valuec[.] on this element of the set {0, ±1, ±j} which has the smallesteuclidean distance or squared error with respect to the scaled tap valuec[.].

After the quantization, the quantized tap or training values c₅[.] arestored in the ROM 18. The preprocessing described so far may beconducted prior to the actual timing procedure since the content of theC64 symbol is standardized and known a priori on the receiver side.

The first step in the actual timing procedure is to conduct the matchedfiltering within the correlation unit 20. For this purpose, thequantized pentenary training signal <C₅>as well as the parameters k_(S),k_(E) are read from the ROM 18 into the correlating unit 20. In thecorrelation unit 20, matched filtering is performed in accordance with

${{C\lbrack k\rbrack} = {\sum\limits_{\mu = 0}^{N_{C64} - 1}{C_{5}*{\lbrack\mu\rbrack \cdot {r_{D}\left\lbrack {\mu + k} \right\rbrack}}}}},{k = k_{S}},\mspace{11mu}\ldots\mspace{11mu},\left( {k_{E} + N_{CP}} \right)$where C[k] designates the estimated channel impulse response, c₅*designates the complex conjugated quantized tap value comprised withinthe pentenary training signal <c₅>, r_(D) designates a sample valuecomprised within the receive signal and k designates a specific momentin time.

The estimated channel impulse response C[k] constitutes the correlationresult or matched filter output of a single correlation operation.Altogether, a number of (k_(E)+N_(CP)) −k_(S) correlation or filteringoperations are performed. During each correlation operation, a part ofthe receive signal comprising the receive signal samples r_(d)[k],r_(D)[k+1], . . . r_(D)[k+N_(C64)−1] is correlated with the processedtraining signal <c₅> corresponding to the sequence of tap values c₅[0],c₅[1], . . . c₅[N_(C64)−1].

Having obtained the channel impulse responses C[k] in acomplexity-efficient manner as described above, the remaining part is toderive the best possible timing instant from the channel impulseresponses C[k]. As is shown in R. van Nee, R. Prasad, OFDM for wirelessmultimedia communications, Artech House, 2000, the solution to thetiming problem is to find the location of a window of length N_(cp)+1within the hatched portion depicted in FIG. 3 such that the energy ofthe channel impulse response C[k] contained within this window ismaximized. This process is performed within the detection unit 22.

In the detection unit 22, the energy E_(win)[k] contained within eachspecific window of length N_(CP)+1 is calculated in accordance with

${E_{wln}\lbrack k\rbrack} = {\sum\limits_{i = 0}^{N_{CP}}{{{C\left\lbrack {i + k} \right\rbrack}}^{2}.}}$

The estimated timing instant k_(C64) corresponding to the begin of thefirst C64 symbol depicted in FIG. 2 is given byk _(C64)=arg max_(k∈{k) _(S) _(, . . . , k) _(E) _(}) {E _(win) [k]}.

The maximum window energy E_(win,max) for the optimum timing instantk_(C64) can be defined asE _(win,max) :=E _(win) [k _(C64)].

The value of E_(win,max) is output to the detection unit 24 where falsealarm detection is performed. False alarm detection aims at detectingwhether the currently processed part of the receive signal is really dueto the transmitted preamble or whether the initial acquisition or timinginformation has failed. False alarm detection is based on the fact thatthe encountered energy after matched filtering or correlation issignificantly higher in the “right alarm” case compared to the falsealarm case.

For simplicity, in the following several assumptions are made:

-   -   an ideal training signal <c_(ideal)> of length N_(C64)=64 is        used    -   <C_(ideal)> shall have ideal auto-correlation properties, i.e.        one peak and zeros elsewhere    -   <C_(ideal)> is used in the transmitter as well as in the        receiver    -   the power density spectrum of the received sample stream <r_(D)>        is white    -   no noise is imposed    -   a one-tap channel is considered.

The right alarm case is considered first. For ideal synchronization andideal Automatic Gain Control (AGC), the correlation elements provide thesquared magnitudes of the elements of <c_(ideal)>, which are in theaverage equal to the mean power of the training signal P_(c,ideal).Thus, the amplitude of the correlation peak is equal to the length of<C_(ideal)>, namely N_(C64)=64, times P_(c,ideal). The energy windowafter correlation contains exactly the peak and zeros elsewhere. Hence,the window energy for right alarm isE _(win,right) =N _(C64) ² P _(c,ideal) ²=4096P _(c,ideal) ².

In the false alarm case the received sample sequence <r_(D)> isuncorrelated to the transmitted <c_(ideal)>. Every correlation result isof the form

$C = {\sum\limits_{\mu = 0}^{N_{C64} - 1}{c_{ideal}*{\lbrack\mu\rbrack \cdot {{r_{D}\lbrack\mu\rbrack}.}}}}$

To determine the average window energy in the false alarm case theexpected value of the squared magnitude of C is needed. It yieldsE{|C| ² }=N _(C64) E{|C _(ideal)|² }E{|r| ² }=N _(C64) P _(c,ideal) P_(r),where the assumptions that <c_(ideal)> and <r_(D)> shall be whitesequences were used. As can be seen from

${{E_{wln}\lbrack k\rbrack} = {\sum\limits_{i = 0}^{N_{CP}}{{C\left\lbrack {I + k} \right\rbrack}}^{2}}},$each element in the energy window has the average power E{|C|²}. Hence,the average window energy for false alarm isE _(win,false)=(N _(CP)+1)·N _(C64)·_(Pc,ideal) ·P _(r)=1088·P_(c,ideal) ·P _(r).

Of course, this derivation holds only for the assumptions illustratedabove and only provides the principles of a false alarm detection whichis based on energy calculations. In real reception, impairments likenoise, a non-ideal training signal, and multipath propagation have to betaken into account. The mean power of the training signal <c₅> at thereceiver may be different from that in the received sample streamdependent on the AGC setting. Thus, the relevant energy terms regardingfalse alarm detection have to be rewritten asE _(win,right) ≦N _(C64) ² ·P _(c,5) ·P _(r and)E _(win,false)≈(N _(CP)+1)·N _(C64) ·P _(c,5) ·P _(r).

Based on these energy terms an energy threshold (E_(threshold)) for thewindow energy can be defined such that it becomes very unlikely thatright alarms are discarded but that there will be still a sufficientlyhigh false alarm detection rate.

It may be well understood that the timing and quantization principlesdescribed above are not restricted to maximizing the signal power withinthe guard interval. One could also think for some receiver algorithms ofmaximizing the energy in a window having a size different from the guardinterval length. It is also possible to combine several different timingstrategies to get different timing instants which might then be selectedby other criteria dependent on the post processing algorithms.

1. A method in a wireless communication system of providing timinginformation for a received transmit signal, comprising providing atraining signal relating to a known signal portion of the transmitsignal; scaling the training signal with a variable scaling factor;quantizing the scaled training signal; correlating one or more parts ofthe received transmit signal with the scaled training signal to obtainone or more correlation results; and determining the timing informationon the basis of the correlation results.
 2. The method according toclaim 1, wherein varying the scaling factor is used to control acomplexity of the correlating.
 3. The method according to claim 1,wherein the training signal comprises complex training values andwherein a real part and an imaginary part of each training value arequantized jointly.
 4. The method according to claim 3, wherein, duringquantization, the training values are mapped on a predefined set of purereal and pure imaginary values.
 5. The method according to claim 4,wherein the predefined set of pure real and pure imaginary valuescomprises a value zero.
 6. The method according to claim 5, wherein thescaling factor is varied to adjust the number of training values mappedon the value zero.
 7. The method according to claim 1, wherein theprovided timing information is an optimum timing instant forsynchronization purposes.
 8. The method according to claim 1, whereinthe one or more parts of the receive signal are correlated with thescaled training signal by means of a matched filter.
 9. The methodaccording to claim 1, wherein one or more correlation results in theform of estimated channel impulse responses are obtained.
 10. The methodaccording to claim 9, wherein, for each possible timing instant, achannel impulse response signal power contained in a respective timewindow of the received transmit signal is determined.
 11. The methodaccording to claim 10, wherein the step of determining the timinginformation on the basis of the correlation results comprisesdetermining the time window containing the maximum signal power.
 12. Themethod according to claim 10, wherein based on the maximum signal powera false alarm detection is performed.
 13. The method according to claim12, wherein the false alarm detection comprises comparing the maximumsignal power with a signal power threshold.
 14. A computer programproduct embodied in a tangible medium comprising program code portionsfor performing the steps of claim 1 when the computer program product isrun on a computer system.
 15. The computer program product according toclaim 14 stored on a computer-readable recording medium.
 16. A receiverof a wireless communication system for receiving a transmit signal,comprising a unit for providing a training signal relating to a knownsignal portion of the transmit signal; a unit for scaling the trainingsignal with a variable scaling factor; a unit for quantizing the scaledtraining signal; a unit for correlating one or more parts of thereceived transmit signal with the scaled training signal to obtain oneor more correlation results; and a unit for determining timinginformation on the basis of the correlation results.
 17. The receiveraccording to claim 16, wherein the training signal comprises complextraining values and wherein the unit for quantizing the scaled trainingsignal jointly quantizes a real part and an imaginary part of eachtraining value.
 18. The receiver according to claim 16, furthercomprising a unit for detecting a false alarm on the basis of a maximumsignal power contained within a time window of the received transmitsignal.
 19. A receiver of a wireless communication system for receivinga transmit signal, comprising: means for providing a training signalrelating to a known signal portion of the transmit signal; means forscaling the training signal with a variable scaling factor; means forquantizing the scaled training signal; means for correlating one or moreparts of the received transmit signal with the scaled training signal toobtain one or more correlation results; and means for determining timinginformation on the basis of the correlation results.
 20. The receiveraccording to claim 19, wherein the training signal comprises complextraining values and wherein the means for quantizing the scaled trainingsignal is configured to jointly quantize a real part and an imaginarypart of each training value.